EMC’09/Kyoto
23P3-3
Left-Handed Transmission Line Characteristics
Made by F-SIR Structure on PCB
Ryosuke Yanagisawa1, Yoshiki Kayano2, Hiroshi Inoue3
Faculty of Engineering and Resource Science, Akita University
1-1 Tegatagakuen-machi, Akita 010-8502, Japan
1,2
{yanagisawa, kayano}@venus.ee.akita-u.ac.jp
3
[email protected]
Abstract—Basic left-handed transmission line (LH-TL)
characteristics made on PCB is an important future issue for the
application of the EMC field. In this paper, possibility of a LHTL characteristic made by a folded-stepped impedance resonator
(F-SIR) type is investigated experimentally and theoretically as a
first time. The calculations by FDTD and/or FEM (HFSS) show
the usability of the LH-TL. The experimental results indicate
some back-ward propagation characteristic but the differences
with the calculation is still existed.
CL
LL
(a) purely left-handed
CR
LL
(b)composite-right/left-handed
Fig. 1 Equivalent circuit model of left-handed transmission line.
Key words: Left-handed transmission line, printed circuit board,
folded-stepped impedance resonator, back-ward propagation
I. INTRODUCTION
Recent electronics systems which are essential to
information technology society are getting smaller and
operating in very close to each other. Near field problem not
only far-field issue is very important factor for the mutual
interference, so called intra-EMC problem. Ultimate problems
may exist in the IC itself. Alternatively, new method and/or
material structure are wanted to see in near future for the
suppression and filtering to the EMC problem. The
application of the meta-material and/or the left-handed (LH)
medium, which has equivalently negative permittivity and
permeability and refractive index, should be investigated for
the near future solution of the EMC problem [1].
As an expression of the equivalent circuit is shown as
ladder circuit of capacitance and inductance and can be treated
in the transmission theory, new applications for microwave
circuits which have left-handed transmission line (LH-TL)
and peculiar electromagnetic (EM) responses have been
proposed [2]-[7]. Therefore, it is also expectable if LH-TL is
constructed in ICs and on Printed Circuit Board (PCB), wide
innovative progress should be performed.
In this paper, one of basic experimental and theoretical
approaches for the breakthrough to apply the LH-TL
characteristic designed on the PCB will be demonstrated. It
has a possibility to show back-ward propagation characteristic.
The structure used as under test is described in the section II.
Experimental and numerical analysis methods are explained in
the section III. The results of the experiment and calculation
are shown, and the difference of the both results are also
discussed in the section IV.
LR CL
II. MODEL STRUCTURE OF THE LH-TL BY F-SIR
A. F-SIR Structure
A generalized simple model is indispensable to achieve the
LH-TL with back-ward characteristic. The purely left-handed
transmission line is constructed of series capacitor CL and
shunt inductor LL as shown in Fig. 1(a). However, a purely
LH-TL structure does not exist. One of the structures having
the LH characteristics is composite right/left-handed
transmission line (CRLH-TL) [3]. CRLH-TL is consisted of
right-handed and left-handed transmission lines as shown in
Fig. 1(b). At lower frequencies, CRLH-TL corresponds to
purely LH-TL. To construct a CRLH-TL on microstrip line, it
is necessary series capacitor and a shunt inductor in the
transmission line representation. So far, CRLH-TL is
implemented in inter-digital capacitor and stub inductor on
microstrip line structure. This method requires shorted via.
Since such via becomes a serious problem in the fabrication
process, the CRLH-TL without via has been proposed by
using conductor-backed coplanar strips [8].
On the other hand, folded-stepped impedance resonator (FSIR) structure has some advantages in microwave filter [9],
[10].Key features of SIR are as follows:
(1) A wide degree of freedom in structure and design
(2) A wide range of applicable frequency through the use
of various types of transmission line
(3) Possibility of down sizing
(4) Low loss
(5) Easier design by changing length and width of the
resonator
So the SIR can be applied not only to filters but also to LH-TL.
Consequently, conductor-backed F-SIR structure, as shown in
Fig. 2(a), is chosen as transmission line implementation.
Figure 2(b) shows equivalent circuit model for periodic F-SIR.
Copyright © 2009 IEICE
645
EMC’09/Kyoto
23P3-3
The gap between F-SIR and input/output lines is expressed as
series capacitor. The gap between F-SIRs is also expressed as
series capacitor. The F-SIR is expressed as RLC-parallel
resonant circuit, where the shunt resistance Rp is disregarded
in this paper. At lower frequencies (below parallel resonant
frequency), F-SIR is behaved as shunt inductor. Hence LH
characteristics are achieved by periodic F-SIR structure.
F-SIR
Cs
Cs
s
Rp
Cp
Lp
Rp
Cp
Lp
B. Model for the Discussion
Figure 3 shows F-SIR model under test. (a) is the layout,
(b) and (c) are photograph. The PCB consisted of conductor
backed coplanar strip line. The PCB has two layers, with the
upper layer for the signal and ground traces and the lower
layer for the reference (ground) plane. The size of PCB is
114mm length, 90mm width, and 1.53mm thickness of the
dielectric substrate with a permittivity of εr=4.5. The trace,
with 2.0mm width, is located on the dielectric substrate. The
distance of gap between the F-SIR and the input/output lines
is 2.0mm.
III. EXPERIMENTAL AND MODELING METHODS
(a)
Periodic F-SIR
(b) Equivalent circuit model for periodic F-SIR
Fig. 2 F-SIR Structure.
y
z
s=2.0mm
w = 90 mm
input line
x
output line
wr=36mm
Port1
Port2
via
ground line
wt = 2.0 mm
lt=10mm
FR-4 (εr = 4.5)
l = 114 mm
(a) Layout
A. Experimental Method
The experimental method, usually used for transmission
line on the printed circuit board, is applied to the developed
samples. The transmission coefficient (magnitude |S21| and
phase <S21) was measured using a network analyzer (Agilent
E8358A). The network analyzer is calibrated on the tip of the
connector. The measured frequency range was from 300kHz
to 9GHz.
At general measurement for Scattering-parameters, ends of
the transmission lines should be terminated with its
characteristic impedance. Although the ends of lines are
connected to 50Ω−port, 50Ω is not matched to the
characteristic impedance of the transmission line. However, it
is considered that the estimation of the transmission
characteristic is possible.
A dispersion diagram is plotted using Eq. (1). A group
delay τg is calculated by using Eq. (2).
βd = − ∠S 21
(1)
τg = −
(b) photograph (top view)
∂φ
1 d∠S 21 ( f )
=−
∂ω
2π
df
(2)
B. Numerical Modeling
Two numerical methods are used for numerical analysis.
One method is finite-difference time-domain (FDTD) method.
An analytical space was composed from non-uniform size of
the cells. The size of cells in coarse region are Δx=0.2, Δy=2.0,
Δz=2.0mm and that in fine region near the signal trace and
dielectric substance is Δx=0.2, Δy=0.2, Δz=0.51mm,
respectively. PML of 12 layers was used for the absorbing
boundary condition. The metal is modelled as a perfect
electric conductor without thickness.
Other method is finite element method (FEM). In this paper,
commercial software (ANSOFT, HFSS) is used for FEM
calculation.
IV. RESULTS AND DISCUSSION
(c) photograph (bottom view)
Fig. 3 Layout of designed F-SIR on the PCB under test.
A. Measurement and Field Simulation
Frequency response of transmission coefficient |S21| is
shown in Fig. 4. The solid, broken and chain lines indicate
measured, FDTD and FEM calculated results, respectively.
Result indicates that F-SIR structure has the narrow LH pass-
Copyright © 2009 IEICE
646
EMC’09/Kyoto
23P3-3
band at around 0.9GHz (Measured: 900MHz, FDTD:
788MHz and FEM: 857MHz) and also right-handed passband around 3.4GHz. These results indicate that F-SIR
structure can construct CRLH-TL. Measured result on
frequency response is approximately similar to those of FDTD
and FEM calculated results. However, measured result |S21| at
LH pass-band is -30dB and is smaller than that of numerical
modeling. This difference may result from losses of dielectric
and metal.
0
Measured
FDTD
FEM
|S 21| [dB]
-20
B. Circuit Approach
Equivalent circuit model provides enough flexibility to
different geometric parameters, and increases the ability to
provide insight and design guidelines. By using the equivalent
circuit model, we attempt to demonstrate the validity of LH
characteristics made by F-SIR structure on PCB.
An equivalent circuit model for F-SIR type transmission
lines is used for calculation of the transmission characteristic
and dispersion diagram. Figure 7 shows the equivalent circuit
model. The equivalent circuit consists of five parts: a source, a
transmission line based on the TEM assumption, electric
coupling due to the gap, LC-parallel resonant circuit due to
the F-SIR, and a termination (load). The capacitances (Cs, Cg
Cp and CR) of circuit parameters are calculated by 3D-field
solver (ANSOFT, Maxwell Q3D Extractor). On the other
hand, the inductances (LL and LR) are calculated by cut-off
frequency [3] of 900MHz and 3.4GHz, respectively.
-40
-60
-80
-100 7
10
10 8
10 9
Frequency [Hz]
Fig. 4 Frequency response of transmission coefficient |S21|.
Frequency [Hz]
Figure 5 shows dispersion diagram. Measured result shows
negative phase-constant below 0.9GHz. This indicates that
proposed transmission line made by F-SIR structure on PCB
has LH characteristic with back-ward propagation. In addition,
measured result in frequency range between 734 - 802MHz
shows negative-slope which means negative group delay
(velocity).
Frequency response of group delay τg is shown in Fig. 6. It
is demonstrated that negative group delay in frequency range
between 734 - 802MHz is achieved. On the other hand, there
is no negative group delay characteristic in FDTD calculated
result.
10 9
LR
LR
Rin
10 8
Rout
Cg
10 7
-10
0
10
20
β d [radians]
30
(a)
40
LL
Cg
Model 1
Cp
LR
Cs
Cs
LR
Rin
30
Rout
Cg
Measured
FDTD
FEM
20
CR
LL
Cg
Vin
10
(b)
Model 2
Fig. 7 Equivalent circuit model of F-SIR. LR=17.67nH, Cs=0.124pF,
CR=10.2pF, LL=3.067nH, Cg=3.45pF, Cp=0.0024pF.
0
-10
-20
-30
0
CR
Vin
Measured
FDTD
FEM
Fig. 5 Dispersion diagram.
Time delay τg [ns]
Cs
Cs
1
2
Frequency [GHz]
3
4
Frequency response of |S21| is obtained from the equivalent
circuit model using H-SPICE. Calculated |S21| and dispersion
diagram are shown in Figs. 8 and 9, respectively. The
measured and calculated results on equivalent circuit model 2
are in good agreement up to 2GHz. The model 2 has an antiresonance at 700MHz. So capacitance Cp is important element.
Fig. 6 Frequency response of group delay τg.
Copyright © 2009 IEICE
647
EMC’09/Kyoto
23P3-3
0
βd = cos −1
Result indicates that F-SIR structure has LH characteristic
in frequency range between 0.878-0.890GHz, i.e., LH passbandwidth is 12MHz. Consequently, validity of LH-TL
characteristics is demonstrated.
|S21| [dB]
-50
-100
V. CONCLUSION
The possibility of a LH-TL characteristic made by the FSIR type was investigated experimentally, numerically and
theoretically. The calculations by FDTD and/or FEM (HFSS)
show the usability of the LH-TL. The experimental results
indicate some backward propagation characteristic but the
differences with the calculation is still existed.
The high-Q and wideband LH pass band is required to solve
the practical EMC problem. Further work will be carried out
on this concept.
Measured
Equiv. Cir. model 1
Equiv. Cir. model 2
-150
10 7
10 8
10 9
Frequency [Hz]
Frequency [Hz]
Fig. 8 Frequency response of transmission coefficient |S21|.
ACKNOWLEDGMENTS
The authors express their thanks to Cyberscience Center,
Tohoku University, and General Information Processing
Center, Akita University, for their support with computer
resources. This research was partially supported by the
Ministry of Education, Science, Sports and Culture, Grant-inAid for Young Scientists (B), 19760190.
10 9
10 8
Measured
Equiv. Cir. model 1
Equiv. Cir. model 2
10 7
-10
0
β d [radians]
10
REFERENCES
20
[1]
Frequency [GHz]
Fig. 9 Dispersion diagram.
[2]
0.94
[3]
0.92
[4]
0.9
0.88
A+ D
(4)
2
[5]
Left-handed
[6]
0.86
[7]
0
1
2
βd [radians]
3
[8]
Fig. 10 Dispersion diagram obtained from ABCD-matrix (frequency range
between 0.85-0.95 GHz).
The equivalent circuit model 2 is used to calculate ABCDmatrix (F-parameter). The dispersion diagram is calculated
from acquired ABCD-matrix and Eq. (3) and (4), and is shown
in Fig. 10.
S 21 =
2
A + B / Z 0 + CZ 0 + D
[9]
[10]
(3)
Copyright © 2009 IEICE
648
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